/* S_TANH.C

 * 

 * Portions Copyright (c) 1993-1999 Nokia Corporation and/or its subsidiary(-ies).

 * All rights reserved.

 */

/* @(#)s_tanh.c 5.1 93/09/24 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice 

 * is preserved.

 * ====================================================

 */

/*

FUNCTION

        <<tanh>>, <<tanhf>>---hyperbolic tangent

INDEX

tanh

INDEX

tanhf

ANSI_SYNOPSIS

        #include <math.h>

        double tanh(double <[x]>);

        float tanhf(float <[x]>);

TRAD_SYNOPSIS

        #include <math.h>

        double tanh(<[x]>)

        double <[x]>;

        float tanhf(<[x]>)

        float <[x]>;

DESCRIPTION

<<tanh>> computes the hyperbolic tangent of

the argument <[x]>.  Angles are specified in radians.  

<<tanh(<[x]>)>> is defined as 

. sinh(<[x]>)/cosh(<[x]>)

<<tanhf>> is identical, save that it takes and returns <<float>> values.

RETURNS

The hyperbolic tangent of <[x]> is returned.

PORTABILITY

<<tanh>> is ANSI C.  <<tanhf>> is an extension.

*/

/* Tanh(x)

 * Return the Hyperbolic Tangent of x

 *

 * Method :

 *				       x    -x

 *				      e  - e

 *	0. tanh(x) is defined to be -----------

 *				       x    -x

 *				      e  + e

 *	1. reduce x to non-negative by tanh(-x) = -tanh(x).

 *	2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)

 *					        -t

 *	    2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)

 *					       t + 2

 *						     2

 *	    1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)

 *						   t + 2

 *	    22.0   <  x <= INF    : tanh(x) := 1.

 *

 * Special cases:

 *	tanh(NaN) is NaN;

 *	only tanh(0)=0 is exact for finite argument.

 */

#include "FDLIBM.H"

static const double one=1.0, two=2.0, tiny = 1.0e-300;

/**

Calculate hyperbolic tangent.

@return hyperbolic tangent of x.

@param x Angle expressed in radians (180 degrees = PI radians).

*/	

EXPORT_C double tanh(double x) __SOFTFP

{

	double t,z;

	__int32_t jx,ix;

    /* High word of |x|. */

	GET_HIGH_WORD(jx,x);

	ix = jx&0x7fffffff;

    /* x is INF or NaN */

	if(ix>=0x7ff00000) { 

	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */

	    else       return one/x-one;    /* tanh(NaN) = NaN */

	}

    /* |x| < 22 */

	if (ix < 0x40360000) {		/* |x|<22 */

	    if (ix<0x3c800000) 		/* |x|<2**-55 */

		return x*(one+x);    	/* tanh(small) = small */

	    if (ix>=0x3ff00000) {	/* |x|>=1  */

		t = expm1(two*fabs(x));

		z = one - two/(t+two);

	    } else {

	        t = expm1(-two*fabs(x));

	        z= -t/(t+two);

	    }

    /* |x| > 22, return +-1 */

	} else {

	    z = one - tiny;		/* raised inexact flag */

	}

	return (jx>=0)? z: -z;

}